Residue-number-system (RNS) concepts can be used to obtain digital filter architectures that have attractive features for VLSI implementation due to the modularity that results from the arithmetic. RNS concepts are also of interest for adaptive digital filters that require a considerable amount of computation to be implemented in real time. The authors present designs for an FIR adaptive filter based on the well-known least-mean-squares (LMS) adaptive algorithm. The first design is for the standard time-domain LMS algorithm. The second is for an LMS algorithm that incorporates the Walsh-Hadamard transform to improve convergence rates when the filter operates in a colored noise environment.